The European Spallation Source (ESS) is an intergovernmental project building a multidisciplinary research laboratory based upon the worlds most powerful neutron source. The facility will be built in Lund, Sweden. The ESS will use a linear accelerator (linac), which will deliver pro- tons with 5 MW of power to the target at 2.5 GeV, with a nominal current of 50 mA. Three separate cryoplants are foreseen to guarantee the necessary cryogenic cooling capacity for the entire facility. The super- conducting part of the linac consists of a total of 208 niobium cavities cooled with superfluid helium at 2K. The cryogenic hydrogen moderators in the target will operate at 17K to 20K under supercritical conditions. The test stand and instruments cryoplant combines liquefaction for the instruments at 4.5K and the occasional helium refrigeration for the cryomodule test stand. This article describes the base- line considerations, the conceptual design and the preliminary heat load estimates for the cryogenics of the ESS project.